That is, you don't have a bootable ISO image CD of Ubuntu and assuming that some OS boots...
Your problem is that you want to boot the ISO image on the external HDD to that HDD without burning it to another medium? Why of course, all is possible with linux, but you need a system somewhere that boots.
I might use Ubuntu, once it is installed on the HDD, to make a bootable USB pendrive, allowing you to use the system and its CD burner to download , burn, and install Ubuntu as you like.
Of course, if you do not have, or can not use, a system that boots, you will need a bootable linux image, a CD or USB, from elsewhere.
You might search the forum for how others have used unetbootin. Good Luck
By the way, a nice question.